I moved to FL fall 2018 - currently I am a temp remote employee at a consulting co. based out of MN. Am currently working remote for a client that is based in Mn. Per client request I must travel to MN 1 week a month Jan19-Dec 2019. 12 wks total. I do not pay MN state taxes on my paychecks as I am a FL resident. Do i have any MN state income tax obligation?
For 2019, you must file a MN non resident return and pay MN tax on the income you earned for those 12 weeks.
You do not say where you moved from, in the fall of 2018. Assuming it was MN, you should have filed a part year resident return.